If gravitational torque is a red herring, how do we run fast?

In his comment on my post yesterday, Ewen reported that he has a heart rate around 153 when race walking 1500m in 8 minutes, and a similar heart rate when running 1500m in about 5:40.  He assumes that in both instances he has a similar cadence of around 180 steps per minute, and therefore is able to compute his stride length as 1.04 metres when walking and 1.47 metres when running.  He concludes that walking is not a very efficient form of locomtion – at least at these speeds.  In fact, once we want to move at speed faster than about 7 Km per hour (8.5 min /Km) most people find that running is more efficient (i.e uses less energy per Km at a given speed). This is improved efficiency achieved by becoming airborne during each stride. 

 

If we want to accelerate from rest or from a jogging pace, we can unbalance ourselves by displacing our centre of gravity forward of our supporting foot.  As Jack Nirestein (or Nicholas Romanov) might point out, unbalancing ourselves in this way generates gravitational torque that produces a head forwards and down rotation, so that we naturally increase our speed.  However, gravitational torque is largely irrelevant to the distance runner, because we actually spend most our time running at near constant speed. 

 

Gravitational torque cannot provide forward propulsion at constant speed, because any torque producing a head forward and down rotation during part of the gait cycle must be counteracted by an oppositely directed torque at some other part of the gait cycle if we wish to remain upright.  In fact, allowing an appreciable gravitational torque to develop at any point in the gait cycle when running a constant speed is actually inefficient because the need to apply a force to reverse that torque results in waste of energy. 

 

So how can we minimize the wasteful generation of gravitational torque?  Perhaps it might seem paradoxical but we do this by becoming airborne. If we spend an appreciable fraction of the gait cycle in the air, we minimize the effects of gravitational torque because gravity can only exert a torque when a part of us is anchored to the ground.  However becoming airborne also uses energy.  Due to elasticity of muscles and tendons at footfall we can recover some, but not all, of the energy spent lifting ourselves upwards against gravity.  So, if we wish to run we are faced with one of two alternatives: spending energy lifting ourselves upwards to become airborne only to see an substantial fraction of this energy dissipated as we fall back to earth, or allowing gravity to rotate us face forwards and downwards, only to have to then apply an opposite torque during the early part of the next stance phase, to correct this rotation.  Running is indeed a dance with a devil named gravity.  Hence the name of the series of articles on the mechanics of running that I wrote last year and have posted in the pages listed in the side bar of this blog: ‘Running: a dance with the devil’.

 

If gravitational torque is largely irrelevant when running at constant speed, what should we do if we wish to maintain a fast pace?  We might consider increasing cadence.  In fact the faster the cadence the less energy we waste on lifting our body against gravity because we fall less during a series of short fast steps than during a series of longer slow steps of the same total duration.  Hence, efficient runners tend to adopt a fast cadence (180 steps per minute or perhaps more) even at slow speeds.  Unfortunately, beyond a certain cadence, rapid turnover is no longer efficient.  I suspect this is because there is a limit to the maximum rate at which the actin and myosin protein filaments that form the contractile machinery within our muscle fibres can cycle through the sequence of engagement, ratcheting and release that occur when a muscle contracts.  So once we have reached maximum cadence, which might be 180 steps per minute or maybe 200 steps per minute for some people (eg Haile Gebresalassie) what can we do?  Most of us reach near maximum cadence at all speeds faster than a jog.  If we want to go any faster than a jog, we must increase stride length.

 

But this is where the task become a bit tricky.  If we reach out with our leading leg before footfall so that we strike the ground with the foot well in front of the centre of gravity, we suffer a braking force that places great stress on joints; dissipates our momentum; and places us in a position where gravity exerts a backwards torque.  So reaching out with the leading leg is both dangerous and inefficient.  As almost all experts on efficient running emphasize, at footfall the foot should be moving backwards relative to the body so it touches down at near zero speed relative to the ground, as near to directly underneath the centre of gravity as possible (though it must touch down at least slightly in front of the COG if we wish to remain upright unless we are running into a very strong headwind).

 

If we cannot afford to reach forwards, how can we increase stride length?  The answer is by propelling ourselves higher into the air at lift off.  In fact, most of the force that generates the upwards propulsion is actually delivered mid stance – during the latter part of stance the centre of gravity is already moving upwards as we remove the weight from the supporting foot.  Once we are airborne momentum carries us forwards, without need for forward propulsion except to overcome wind resistance.  So the answer to going faster than a jog is simply to push up more strongly in mid stance.  Probably about 50% of this push can be obtained from elastic recoil, but elasticity is far from 100% efficient, so we must achieve a substantial l part of the required work be achieved by active muscular contraction.  That is why we need to be fit to sustain a fast pace.  No amount of skillful technique can replace the need to be fit if we want to run far and fast.

 

So why bother with technique?  In fact many elite runners over the years have simply replied ; ‘don’t bother; just get fit’ or words to that effect.  I wasn’t an elite athlete or even a serious competitor.  I was actually far more interested in mountaineering during the years when I might have achieved my peak as a runner, but I did run marathons in less than two and a half hours without ever spending a minute thinking about technique.  Furthermore, I rarely suffered any injury.  I am inclined to think that was probably due to the fact that carrying a heavy pack up and down hills and mountains had given me a fairly rugged frame.

 

So why do I now have a blog with the words ‘Efficient Running’ in the title?  Because as I approach my mid 60’s I no longer have the natural bounce that used to propel me upwards on each stride with relative ease, and because I no longer have the rugged frame that allowed me to run 100 miles a week without thinking about injury, forty years ago.  I now need to pay more attention to just how it is done. 

 

I certainly do not yet know how it is best done, though I suspect that there is no single answer that will fit the needs of every individual, or indeed all of my own goals.  I appreciate the comments that people make and I am learning.  At this stage, I am fairly certain that merely increasing my cardiac output by aerobic training will not be enough.  I believe that I need to increase my muscular strength, but I also need to know how to apply that strength to best effect. 

 

I believe that I need to increase the power of eccentric contractions in my quads and calves to allow me to capture energy at footfall and return it with added push in mid-stance to initiate the next airborne phase.  I suspect that this should not be a conscious push.  Indeed, while I think the theory of Pose is misguided, I think that Nicholas Romanov’s emphasis on the subjective sense of a quick, light footfall is probably the best subjective experience to aim for, if one is to become airborne quickly enough.  However, because I would like to be still  running in my eighties, I am also concerned about the possibility that too much eccentric contraction (running fast and far too often) might produce lasting microscopic damage.  I am intrigued by the possibility that increased antioxidants in the diet might diminish this risk.

 

Although upward propulsion is paramount, getting airborne is not the only role of the legs muscles when running.  It is also necessary to get the swinging leg forward quickly so that it is in position to support the body at subsequent footfall.  This requires two actions. The first is acceleration of the leg forwards relative to the torso.  This is probably achieved best by a well coordinated simultaneous contraction of the hamstrings (to flex the knee) and the hip flexors, such as iliopsoas.  The second action is a neatly timed deceleration of the swinging leg relative to the torso, so that it drops to the ground just slightly in front of the centre of gravity, with the foot moving backwards relative to the torso and at near zero velocity relative to the ground.  This action requires an eccentric contraction of the hamstrings, together with a gentle tensioning of the quads to modulate the action.  The quad tensioning needs to be subtle, so that the leg is not too stiff on impact, if minimizing risk of injury is a priority.

 

While I am fairly confident with this outline of the muscular actions, there are many subtleties, such as contraction of the hip abductors (mainly glutes) in mid-stance to prevent the pelvis tilting down on the unsupported side.  Even more important is the question of the mental image required to achieve this series of muscular contractions with a degree of fine control that defies conscious direction.  So I still have much to learn.

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64 Responses to “If gravitational torque is a red herring, how do we run fast?”

  1. Ewen Says:

    Canute, thanks for a most interesting post.

    I’ve noticed a decline of natural bounce even at age 51. My youthful body used to give me a ‘free ride’, such that I feel at times I’m training harder than I did then, but running slower. That’s why I’m interested in possible changes to technique or training methods with a view to continuing to ‘race well’.

    It’s interesting that in your mountaineering days you didn’t bother with technique yet still ran well. Perhaps you would have run even faster with ‘good’ technique? I know with teenagers who are new to running it’s relatively easy to improve their technique, but it’s hard to quantify what difference this makes. I’ve seen such runners hold their form at the end of races and/or speed up to win a race by a few metres. Running with good technique may have put them in a position to win a race by not using so much energy mid-race.

    I suspect that technique may have to change to some degree as we age (not sure how much) to make allowances for less recoil from the muscles. I’ve read that as we run faster (up to a certain speed), we become more economical (use less oxygen) because we run with more ‘tension’ in the muscles (on landing and push-off), so there’s more natural recoil. I’m not sure if this means there’s more benefit by doing more training at those sort of paces.

    By the way, I found a video clip of slide accidents which shows the gravitational torque (on some of the accidents) you mentioned in the previous post:

  2. rick Says:

    Canute you say that gravitional torque does not apply when running when going at a steady pace, i think this is where you shoot yourself in the foot as they say and blow your theory to a thousand peaces!
    It is impossible to run at a steady pace, running is a series of accelerations and braking, each time the foot lands it is grounded to the floor and the hip moves over it, the foot is at zero speed yet the body is moving forward, each time the foot lands there is a braking effect before another acceleration, RUNNING CAN NEVER BE AT A STEADY PACE.
    INTERESTING READING BUT YOUR THEORIES ON GRAVITY DO NOT HOLD UP! THEY FALL DOWN WITH GRAVITY!!!

  3. canute1 Says:

    Ewen, Thanks for your comments. I think a stiffer leg due to greater tension in the quads can partially compensate for loss of elasticity, but possibly at the cost of greater risk of damage to the leg.

    Rick, I agree that we speed and slow on every step. That is the unfortunate consequence of gravitational torque, as descibed in my post. Of course you might quite reasonbly state that the head forwards and down torque is useful while it is the reverse torque that is is harmful, but the fact is that they must balance, and in the process, you waste some energy due to internal friction, so you should try to minimize both. To run efficiently you should spend as little time on the ground as possible to minimse the wasteful speeding and slowing. However spending more time in the air creates two problems. We expend more energy getting airborne and we need to transmit greater forces through the foot, creating a risk of meta-tarsal stress fracture. So it is necessary to work out the best compromise.

  4. rick Says:

    Nirenstein addresses all issues above with his method, landing further back puts you off balance and lets gravity pull you forward and using a fast leg turnover means you use the power of gravity more often , the real acid test is out on the road where running using his method produces a faster easer- speed, his method feels right from the first time you use it!
    On Ewen’s straight leg, this is the best way to land, shock should be absorbed through the arch of the foot, i have used a straight knee landing for many years without knee problems, in fact your knee is a much stronger joint when folly straight than if it were bent!
    there is no evidence to prove bent knee running improves injury prevention, its a bit of a myth just like a cadence of 90 is best for everyone or THAT you can can find your max heart rate by taking your age from 220 !
    Canute, good luck with your voyage to find the ideal running method, I,m sure you will find it one day just as i did!
    oH WELL THE ROAD AWAITS !!!

  5. rick Says:

    Here are 2 more tips to help the aging runner ru faster and for longer into their old age;
    1/ weight training will increase bone density, strengthen ligaments, tendons and muscles, increase growth hormone and testosterone! use a good muscular endurance program that covers the main muscle groups.
    2/ plyometrics http://en.wikipedia.org/wiki/Plyometrics
    as used by SEB COE will put a spring back in your step and help you run faster!

  6. canute1 Says:

    Rick,Thanks for those comments. I agree about the value of weight training, though so far I have only done high repetition body-weight resistance exercises. However I agree with all of the advantages you list for resistance training. I am less sure about plyometrics. I believe there are strong reasons to propose that plyometrics will improve speed, but I remain concerned about the evidence for long term damage to muscles even in the absence of overt injury. Therefore, I do only a very small amount of plyometric work.

  7. rick Says:

    A QUESTION FOR CANUTE,
    In your post you seem to be saying that a force cancels out another force and that is a bad thing as far as using gravity to run faster, I put it to you that in fact the opposite is true,
    example a space rockets engines send a thrust of power down to the ground in return the earth pushes back at the rocket and it takes off!
    example 2 a runners foot pushes down into the ground in return the ground pushes back at the runner!
    example 3 using nirensteins method you land behind your center of gravity, gravity pulls you forward, in return your grounded leg is pushed down and back into the ground. on the road this is a positive result to run faster, unless you are running x/c race and you grounded leg slides back and down into the mud and momentum is lost, as happened to me, i asked mr nirenstein about this and he said on mud or sand one must use the hamstrings to pull your foot out of the mud, i also think one needs to land more over your center when running on mud!
    Anyway i have made more improvements with gravity running, now running almost half a mile an hour faster in my tempo run than last summer!

  8. rick Says:

  9. canute1 Says:

    Dear Rick
    The equal and opposite forces of the rocket engine (or indeed of any form of propulsive force) are simply the action and reaction that Newton described in his third law of motion: ‘action and reaction are equal an opposite.’ These equal and opposite forces act simultaneously, one pushing against the other. However the need to match a head forward and downward torque applied when the centre of gravity (COG) is in front of the point of support, with an oppositely directed torque when the COG is behind the point of support raises a different issue. In this situation, the the two forces we are dealing with are acting at different times and on account of internal friction in body tissues, result in an inevitable waste of energy. (The simulataneous ‘equal and opposite force’ that opposes gravity when running, as predicted by Newton’s third law, is in fact part of ground reaction force.)

    I disagree with Nirenstien’s explanation of his technique. However, the potentially good thing about Nirenstein’s method is that it encourages placement of the foot only a slight distance in front of the COG. Consequently, the foot only needs to sustain a substantial force on the ground for a short period after the COG passes over the point of support and total time on stance can be short. This is efficient, and I suspect might be the main reason for your improved performance since taking up the Nirenstein method. It is of course a little bit risky to spend only a very short time on stance because the forces on the foot rise in inverse proportion to the time on stance, and the risk of metatarsal stress fracture increases. This is a rare injury but a major nuisance if you are unlucky enough to suffer it.

    As you remarked the thing that matters is improved performance and if Nirenstien’s method has allowed you to achieve that, that is great. Performance is more important than theory. The main reason why I am eager to understand the mechanics underlying running technique is that it allows me to weigh up the risks and benefits of different styles. For someone with life long problems with my feet and knees who nonetheless wants to continue running in advanced old age, it is important to find a style that achieves the optimum balance between performance and safety. If I simply wanted to maximize performance I would run BK method, but as far as I can see that method places great stress upon joints and muscles. Perhaps the greatest handicap to top performance is injury.

  10. Simbil Says:

    Hi Canute,

    I’ve been meaning to comment on gravitational torque for a while now as I think it makes more sense to me now and I can see why runners do not face plant and also do not have to overstride to correct the torque and avoid face planting. I have not re-read the articles and comments but am going from memory of our previous communications.

    When a runner is on support from mid stance to a little after mid-stance, gravitational torque produces a forwards and downwards rotation of the GCM around the support point (foot). The following period up to terminal stance sees a sharp decline in GRF and the leg begins recovery.
    The leg recovery is the all important balance to gravitational torque. The runner enters the flight phase and the recovery of the leg from a rearward position back to alignment with the body is done whilst there is no ground contact. To swing the leg forward causes a torque to act on the body that moves it upwards and backwards. This is a major correction for the forwards and downwards movement whilst on stance.
    I suspect landing a little ahead also plays a part, but the swing is of most interest to efficient running as it is necessary anyway.
    In summary, of course gravity does not give a free ride, but working with it rather than ignoring it’s effects is where efficiency improvements and injury resistance can be gained.

    • canute1 Says:

      Simbil,
      Thanks for your comment. While it is tempting to wonder if the ‘face forward and down’ torque applied when the point of support is behind COG might be reversed while the body is airborne, unfortunately this is not possible, because a torque requires the application of a external force that produces rotation about a pivot point. When the body is airborne there is no pivot point, and muscular forces exerted within the body cannot produce a torque that imparts angular mometum to the body.

  11. canute1 Says:

    Simbil, When I responded last night, it was after returning home from work late and my response was brief. I now have a few more minutes before going to work this morning. You might reasonably expect some justification of my assertion that torque requires applicatio of an external force at about a pivot point. In terms of basic laws of physics, this is a consequence of the law of conservation of angular momentum. A body can only change its angular momentum if oppositely directed angular momentum is imparted to another object. Apart from the small effects of drag from air-resistance, when we are airborne we cannot impart angular momentum to another object.

    When we run due east we actually cause the earth to slow imperceptibly as it spins around its north-south axis and cause the day to lengthen slightly, in late stance, but than at foot fall, we reverse this effect, so unfortunately we cannot lengthen the day by even a tiny amount by running east, and in fact will only shorten the duraton of daylight as we flee the setting sun.

    It is not easy to provide every day illustrations of these effects because most of us do not have daily experience of isolated rotational motion. A somewhat paradoxical illustration is provided by an acrobat or high-board diver executing an airborne summersault. As the acrobat pulls his body into a tight ball he spins faster. This is because the moment of momentum of a body (the angular equivalent of mass) is proportion to the distance of the mass of the body from the axis of rotation. Therefore to maintain the angular momentum of the spinning airborne body when the mass of the body is pulled nearer to the centre of rotation, the body must spin faster. Similarly, immediately after lift off from stance, a runner will actually start to spin slightly faster in a face forward and down direction as his trailing leg is drawn up towards the axis of the rotation.

  12. Simbil Says:

    Hi Canute,

    Thanks for the response and apologies for the long delay, I’m snowed under at the moment.
    I’ve since had a re-think on this issue (again) and realise my comment can not work in the way I thought it might – more on that at the end of the post.

    Firstly though I would like to look at the torque mechanisms. In running there is a forward torque induced by gravity whilst on support from mid stance to some point between mid and terminal stance and I think we both agree the rotation caused by this torque has to be dealt with to avoid an eventual face plant.
    There are various mechanisms that could deal with this issue; forward landing, toe-off and leg swing whilst on support.
    I think you suggest that a landing ahead is the main mechanism and I think it probably plays a part tough the inherent problems with a forward landing make it far from desirable.
    Some runners use a toe off – a push at terminal stance cause the hips to move forward and the upper body to move backwards; a counter rotation of that experienced previously on stance due to gravitational torque. This is particularly noticeable in runners driving off from the blocks when the lean angle is very large.
    Finally, there is leg swing. Whilst on stance with one leg, the other leg swings forwards. The forward swing of the leg pushes back at the hips and as the hips are supported by the grounded foot, the whole body is rotated backwards around the foot pivot point.
    So it is conceivable that the forward gravitational torque is balanced by this rearward torque from leg swing in that one acts and then the other acts so that the net effect is balance. I think this is probably the main stabilising mechanism in efficient running and allowing a ‘fall’ can automatically force a subconscious swing (and could force a subconscious overstride or toe off too depending on the runners habits and degree of ‘fall’).

    My original point I now realise cannot work – not really for the reasons you gave, more because the torque of pulling and swinging the leg when not on support causes a counter torque that sends the upper body forwards – not a backwards balancing torque as I suggested i.e. pulling and swinging whilst unsupported has the opposite effect to a toe-off.

    Hope that makes some sense.

  13. canute1 Says:

    Simbil,
    As you say, we agree that gravitational torque acting the second half of stance must be corrected. However we achieve this correction, we can only change the angular momentum of our body by action interaction with an external object and the work done to apply the reverse torque will have a braking effect. This is one of the inevitable penalties gravity imposes on us. In the absence of a headwind strong enough to correct the face-forward and downwards torque, I think that landing in front of the COG is the most natural way to correct this torque, on the basis of the observational evidence that all runners appear to do it. I was interested to note that at the Loughborough Pose weekend which I had attended, all the Pose coaches, including Dr Romanov, accepted that the length of time from footfall to mid-stance was approximately equal to the time from mid-stance to lift-off. For most of the time before to mid-stance, the point of support is in front of the COG. As we examined the videos of each of us running (including the Pose coaches) the evidence was there in front of our eyes. As far as I could see the only attempt to explain why this did not produce a counter torque was the claim that no substantial weight was borne prior to mid-stance. Yet the fall of the body was arrested during this period. Maybe force plate data is the most direct way to determine whether or not weighting does occur before mid-stance. The weighting will be less abrupt when landing on forefoot with a moderately relaxed knee and ankle than when heel striking, but nonetheless, some weight bearing must occur or the body would collapse. I would really be great to find some force plate data for a Pose runner.
    An addtional point of agreement between us is your statement that the fall automatically enourages the swing. This unconsious promotion of the swing is why I believe that keeping the pelvis forward (ie. avoiding the dreaded K bend in later stance) is helpful. In fact I think that almost all features of the Pose style are helpful in practice. It is the theory of Pose that I think is wrong. Nonetheless, I do believe it can be dangerous to believe in a wrong theory because it can lead to failure to recognise dangers, such as the magnitude of GRF assocated with a short time on stance, and the stress on the foot produced by forefoot landing. Pose is perhaps a little less risky than some other running styles, but nonetheless, it does have significant risks that tend to be ignored by Pose coaches.

  14. Simbil Says:

    Hi Canute,

    Thanks for your thoughtful response. I do not agree entirely with your assertion that a reverse torque requires interaction with an object – an example would be a stunt man wheeling his arms to stabilise his body whilst falling; accelerating a limb creates a counter acceleration on the body. That’s not the main point though, so we can leave that aside if you like.
    I agree that steady state running often produces a symmetrical gait where the time on support ahead of stance is equal to that to the rear. The runner is running at a set pace so does not want any net acceleration and so an equal stride is necessary.
    If we look at accelerated running though, the situation is different. I’ll have to dig out some of the frame sequences but I seem to remember that a runner accelerating out of the blocks lands more or less under their centre of mass – an effect caused by not striding forwards and by the severe lean angle of the runner leaving the blocks. Under these circumstances we see the what runners naturally do to accelerate quickly; lean forwards of support so the net part of the gait has support behind the COM and contrary to many of my fellow Poser’s views, I think they also drive both arms and legs with vigor. This gives the situation where the runner’s lean causes a forward torque and the driving limbs cause a counter torque and to a lesser extent some pushing off towards terminal stance adds a further counter torque. The final effect is that although the runner is leaning very far forwards, each stride straightens them up and after a handful of strides the sprinter has only a modest lean if any.
    In this way I see the gravitational torque being essential to act as a bracing force for moving the body forwards.

    In less extreme cases, acceleration is achieved by a subtle shift of weight forwards so net support shifts very slightly to the rear. Again this gives rise to a net gravitational torque which must be balanced – I think it is the subconscious balancing by leg swing that makes an efficient runner. I think overstride and/or toe off are less efficient ways to balance the torques though they are commonly seen in runners.

  15. canute1 Says:

    Simon
    I think we agree that the value of gravitational torque is in stimulating muscle activity to produce a forward swing. But we must nonetheless correct this torque. My accounts of running have focused mainly on running at a steady state because distance runners spend most of their time at or near steady pace. Somewhat different things happen during acceleration. In this situation the unbalancing produced by gravitational torque is even more extreme and promotes a very strong and forceful forward swing of the leg to avoid a face down crash. As the runner rises to an erect position in the first few strides, work is done against gravity. This work is done by the muscles. Gravitational torque plays a major role in stimulating the required muscular action
    With regard to the need to interact with an external body to produce torque, I am referring to net torque on the body that results in a change in angular momentum. If the law of conservation of angular momentum is to be obeyed, the application of a torque must involve interaction with an external object. What you are describing is an effect acting within a body to cause one part to rotate relative to another. That does not affect the net angular momentum of the body and cannot correct the net face- forward and down angular momentum generated by gravitational torque in the second part of stance.

  16. Simbil Says:

    Canute,

    I think we are in broad agreement – gravity does not do any net work but causes a biomechanical response that causes acceleration. Any benefit derived from gravity must be paid for at some other point in the gait. Gravity provides no ‘free lunch’. But, gravity is not a ‘red herring’ – it is essential, and in understanding that we get closer to a real biomechanical model of running, which is my ultimate aim.

    One point I was trying to make by bringing up accelerated rather than constant pace running was that although the runner starts by leaning far forwards, they straighten up with each step. I don’t think they straighten up by striding out ahead to create a strong rearwards torque and I think this is key to how you view running and the role of gravity. How do you think the runner goes from a steep lean angle to upright within a few steps of starting a sprint race?

    On the point of unsupported changing of net torque, you are of course right. My point was simply that torque can be rearranged in flight by transferring the torque to other body parts. I am not sure if such a mechanism exists in running but thought it worth exploring – equally it might be a red herring 🙂

  17. canute1 Says:

    Simon,
    I have never considered gravity to be a red herring. Indeed I have described running as a dance with the devil – gravity. I did describe gravitational torque as a red herring. Maybe that was slight hyperbole, because like you, I believe that gravitational torque does help stimulate a reflex action of the leg muscles to get the swing leg forward. However I doubt that this reflex action plays a major part in running at constant speed, unless there is a head wind. In general, the effect of gravitational torque is wasteful because it must be compensated.

    As discussed in my post above, I consider that the most important muscular actions in running are: getting airborne; capturing gravitational potential energy at footfall; and getting the swing leg forward quickly. Gravitational torque may promote the third of these, though in view of the fact that the leg swings forward more powerfully at higher speed when time on stance is less and gravitational torque is less, I doubt that the reflex response to unbalancing is the major driver of this action.

    With regard to your question about how a sprinter goes from crouched starting position to vertical within a few strides, I suspect this is largely by exerting a strong downwards push on the ground throughout each stance phase.

    Finally I do not agree with your assertion that ‘a strong rearwards torque is key to how I view running and the role of gravity’. If I were to rank the various muscular actions of running in order of the importance of developing the strength and coordination required for good execution, my ranking would be: getting airborne (against gravity), capturing gravitational potential energy at footfall; getting the swing leg forward quickly; tensing hip abductors to arrest the gravity-induced drop of the unsupported hip during stance; trunk stabilization; arm swing, neck and head stabilization; etc Compensating for gravitational torque is important in the sense that it has to be done to avoid a face down crash, but I regard it as largely an incidental action. The main reason I have mentioned it in my discussion of running technique is to counter the impression created by Nicholas Romanov and Jack Nirenstien and others, that gravity provides net forward propulsion.

    I think we are both trying to obtain a good understanding of the biomechanics of running. The body is an amazing machine and much still remains a subject for debate. However, I am at present fairly happy with the style of running I have adopted. In practice it is very similar to Pose, despite the fact that I think much of the theory of Pose is misguided. I continue to be delighted to see the progress reported by the Pose runners who post on either the Pose thread or the Efficient Running thread on the Fetch site.

  18. Simbil Says:

    Hi Canute,

    There are a few elements to this discussion, so I’ll break it down to hopefully keep it on track.

    You said, “I have never considered gravity to be a red herring. Indeed I have described running as a dance with the devil – gravity. I did describe gravitational torque as a red herring. Maybe that was slight hyperbole, because like you, I believe that gravitational torque does help stimulate a reflex action of the leg muscles to get the swing leg forward. However I doubt that this reflex action plays a major part in running at constant speed, unless there is a head wind. In general, the effect of gravitational torque is wasteful because it must be compensated.”

    Agreed, I think steady state running is more about keeping breaking to a minimum rather than focusing on acceleration.

    You said, “As discussed in my post above, I consider that the most important muscular actions in running are: getting airborne; capturing gravitational potential energy at footfall; and getting the swing leg forward quickly. Gravitational torque may promote the third of these, though in view of the fact that the leg swings forward more powerfully at higher speed when time on stance is less and gravitational torque is less, I doubt that the reflex response to unbalancing is the major driver of this action.”

    That’s all fine apart from the suggestion that gravitational torque is less at high pace, I’m not sure that is the case. Whilst time on stance maybe a little shorter, the angle of deviation is usually larger which would make the torque stronger.

    You said, “With regard to your question about how a sprinter goes from crouched starting position to vertical within a few strides, I suspect this is largely by exerting a strong downwards push on the ground throughout each stance phase. ”

    You misunderstood me here I think. I asked how a runner gets from a net forwardly leaning position to a net vertical position. The runner leaving the blocks may be leaning at 45* to the horizontal and in a few strides the net lean will be small or non-existant. My point here is that in the first few strides there is a mechanism that erradicates the forward lean – I would suggest a rear torque as in previous posts and am interested to see if you agree.

    You said, “Finally I do not agree with your assertion that ‘a strong rearwards torque is key to how I view running and the role of gravity’.
    If I were to rank the various muscular actions of running in order of the importance of developing the strength and coordination required for good execution, my ranking would be: getting airborne (against gravity), capturing gravitational potential energy at footfall; getting the swing leg forward quickly; tensing hip abductors to arrest the gravity-induced drop of the unsupported hip during stance; trunk stabilization; arm swing, neck and head stabilization; etc Compensating for gravitational torque is important in the sense that it has to be done to avoid a face down crash, but I regard it as largely an incidental action. The main reason I have mentioned it in my discussion of running technique is to counter the impression created by Nicholas Romanov and Jack Nirenstien and others, that gravity provides net forward propulsion.”

    Maybe I have the wrong impression. It seems the main mechanism you have cited for balancing the torque is a forwards stride to balance the rearward portion. The impression that I had was that you believe that to be the main mechanism for balancing torque – is that not the case?
    My problem with that is simply that a forward stride creates braking and braking means you then have to put energy into the system to maintain pace – hence the key to steady pace efficiency is to remove braking as much as possible.
    I agree that the creating the airborne phase and the repositioning of limbs are the biggest costs in running and the considerations of torque are much smaller.

  19. canute1 Says:

    Simon, Thank you for your continuing discussion of gravitational torque. It is clear that we agree on many of the issues.

    With regard to the question of whether or not gravitational torque makes a greater or lesser contribution at high speed, it depends on whether the proportional decrease in time on stance is greater than the proportional increase in speed. This will depend on the individual athlete. When I increase pace from 6 min/Km (easy long-run pace) to 3 min/Km (stride-out pace) I decrease time on stance by slightly more than a factor of 2. So for me torque is probably smaller at higher speed. When I am running faster, I am aware of making a greater conscious effort to drive the swing leg forward via simultaneous contraction of hip flexors and hamstrings, and I doubt that reflex response to gravitational torque is the main driver of the swing. For a runner who has a short time on stance even at slow paces, maybe torque will increase as speed increases, though because torque must be reversed within the gait cycle, the wasteful angular acceleration will contribute to lower efficiency at higher speeds.

    With regard to the reverse torque that corrects for face-forwards gravitational torque in the first few strides following a sprint start from blocks, I have never examined videos of sprinters closely enough to know whether or not to get the foot falls forward of the COG. If the trailing leg is far enough behind the leading leg at footfall, the centre of gravity might be somewhat behind the torso, and perhaps behind the point of support. But without careful examination of videos of a sprint start, I would not want to offer a firm opinion. In any case, I suspect that the major force producing acceleration is actually the push back against the blocks rather than gravitational torque.

    With regard the statement in your previous comment that strong rearwards torque is key to how I view running, I accept that this is not what you meant to say. Instead you had meant to say that I regard landing in front of the COG is the main mechanism for balancing torque. That it true, but the more important point is that I regard that when aiming to maximize efficiency, gravitational torque should be minimized as much as possible, because it leads to a wasteful angular acceleration in one direction and then the opposite direction within the gait cycle. However, it can only be minimized by applying a strong push off from stance. Therefore, the limitation of our ability to exert a strong push off limits the extent to which we can minimize torque. Furthermore, because a very short time on stance results in very large forces on the foot, this creates a significant risk of repetitive strain injury during long runs, and it is safer to suffer a small loss of efficiency for the sake of safety. So, on the whole I regard gravitational torque as a minor aspect of running. I consider it to be the penalty we pay in order to avoid massive ground reaction forces. I consider that it impairs efficiency, and that this will be the case however it is corrected.

  20. Simbil Says:

    Hi Canute,

    I’m finding this discussion very enlightening and interesting and do appreciate your comments. Whilst we seem close to agreement in some areas, I think there are still a coupe of things that need clearing up.

    With regard to the question of whether or not gravitational torque (GT) makes a greater or lesser contribution at high speed, you say that you doubt GT produces a strong swing impulse and you could well be right. However, the physics is the important issue and GT allows for a swing to occur. Without GT the forward swing of the leg would cause the body to pivot backwards which would see you falling on your back in a few strides.
    I think the impulse to swing and correct GT is rather complicated and may not happen instantaneously but rather as a constant correction that wavers around a mean point. I agree that time on support at varying paces is an individual matter, though in Pose it tends to be fairly similar up to sprint speeds at which point it decreases.

    With regard to the reverse torque that corrects for face-forwards gravitational torque in the first few strides following a sprint start from blocks, there are some good vidoes here that you can view frame-by-frame: http://www.posetech.com/video/index.php/weblog/examples_of_good_running_form/
    I’ve spent a long time looking at these but would appreciate your views too.
    You mentioned that the major acceleration from the blocks is the push back against the blocks. It sounds like you mean leg extension to push? If so, that would tend to create a rearward torque on the leaning runner plus a linear acceleration in the plane of the runners lean – at best (from memory) I would expect that to be 45* so half of the linear acceleration would be lifting the runner up and the other half forwards. I think a close look at the videos could answer if that is actually the case.

    With regard to your last paragraph above and the points on balancing the torque, you seem to have omitted the most important mechanism – the swing forward of the leg whilst in stance. This is unavoidable in running and as I mentioned above, without GT would not be possible as it would make you fall backwards. As such, I disagree that it impairs efficiency – it just needs to be understood and worked with in the theoretical model.
    I agree to some extent that it is a balancing act though and I agree with your previous point that GT is eclipsed by the cost of getting airborne in running.

  21. canute1 Says:

    Simon,
    Thanks for your further comments. I accept that gravitational torque is related to the action of getting the swing leg forwards insofar as both occur because it is impractical to spend an infinitesimal time on stance. If it was not for the fact that an infinitesimal time of stance would require an infinitely strong push against the ground and result in infinite ground reaction forces, it would clearly be most efficient to avoid spending any time on stance. The leg would move forward at the same speed as the torso and no swing would be required to ensure it was beneath the torso at the next footfall. Thus, both gravitational torque and the need for swing when running at constant speed in the absence of wind resistance are the price of inefficiency. As I think we both agree, getting airborne is the most important muscular action in running at constant speed, and at least when sprinting, one should aim to spend as little time on stance as possible.

    While I agree that swing and gravitational torque are related, I think you are suggesting that generating the swing results in a head-backwards torque and therefore a head forwards gravitational torque is essential to correct for this. I do not think this is the case. While the swing might be initiated by a push back against the ground, resulting in a forward directed component of ground reaction force (GRF) that tends to produce a head-backwards torque, at the same time, the push upwards to become airborne generates a head-forwards torque, because point of the support is behind the centre of mass in late stance. Provided the net push is along the direction of the sloping leg, there is no net torque. Therefore I do not believe gravitational torque is essential to deal with the torque arising from ground reaction forces in late stance. However I agree that if the net head-back torque due to the forward component of GRF were to be greater than the head-forward torque due to vertical GRF, then gravitational torque will contribute to balancing this net torque. I think we need force plate data together with data regarding the angle of the stance leg, to establish the direction of the net torque due to ground reaction force in late stance. The empirical observation that most runners land approximately as far in front of their centre of mass as the foot was behind at unweighting make me think that the push in late stance is usually approximately along the direction of the leg. Perhaps a runner who pushes upwards too vigorously might be in danger of over-striding because this push will exacerbate the effect of gravitational torque.

    With regard to the question of whether or not Pose runners spend longer on stance at slower speeds, I am aware that many Pose coaches advocate spending as little time on stance as possible at all speeds. I agree that this is optimal for efficiency, but consider that it is unwise to give that advice without considering the inevitable increase in GRF with short time on stance. When running long distances, the risks of repetitive strain injuries to the metatarsals and/or the plantar fascia and Achilles tendons are not negligible. I still wonder whether the metatarsal stress fracture suffered by Pose coach, Jack Becker, a few years ago was due at least in part to too short a time on stance.

    With regard to accelerating out of the blocks, unfortunately, the video on the Posetech site would not run on my computer – I probably need different software. However I am inclined to think that because the angle of push back against the block is likely to be along the line from centre of mass to contact with the block, the push will not generate much torque on the first step. To determine the net torque in the subsequent few steps as the sprinter accelerates, I think we would need force plate data and data about the angle of the leg, to determine the net torque. However I would not be surprised if there was a net head-back torque due to large forward directed GRF during this acceleration phase, and if so, gravitational torque would tend to compensate for this as you suggest.

  22. Simbil Says:

    Hi Canute,

    Time on support is an interesting one and as you say there are injury considerations as well as the physics. I will leave that for another day though.

    It seems we have a differing view regarding swing and how it is balanced and I think this may be down to a difference of opinion on the basic mechanics of push and swing. This is how I see them:

    1. Leg swing whilst airborne – creates a forward torque on the torso pivot around the COM
    2. Leg swing whilst on support – creates a rear torque on the torso pivot around the support foot
    3. Push off with foot behind with body in alignment (starting from the blocks) – creates force along the body line
    4. Push off with foot behind with torso upright (pace running) – creates force along the leg line which pushes slightly below the COM causing some rear torque on the torso

    (2) is exactly the opposite of gravitational torque and hence my assertion that GT is essential to allow swing (whilst on support).

    I wasn’t really sure on your point about the swing starting with a push off – maybe you could elaborate on that mechanism?

  23. canute1 Says:

    Simon, You have itemized the points of debate succinctly, but I think perhaps you have over-simplified things, so I am afraid my responses will be more long-winded:

    1. Leg swing whilst airborne – creates a forward torque on the torso pivot around the COM
    Once airborne, actions in which one part of the body is pulled towards another do not create net angular momentum, whereas gravitational torque does, so I do not think internal re-arrangements of the body parts are relevant to the balancing of gravitational torque. Nonetheless, I would expect that the muscle actions that pull legs towards or away from the torso during the airborne phase might produce some net movement of the torso relative to the centre of mass that is small in magnitude but complex. The leading leg is pulled back towards the torso, while the trailing leg is pulled forward towards the torso. I suspect the major net effect on the torso will be a twist around the vertical axis, but this is largely canceled by arm swing.

    2. Leg swing whilst on support – creates a rear torque on the torso pivot around the support foot
    I do not consider that the swinging leg creates torque. As in my response to item 1, I do not consider that internal re-arrangements produced by muscles pulling one part of the body towards or away from another produce any net angular momentum, and are therefore not directly relevant to balancing gravitational torque. However, in early stance the swing leg is behind the torso and is pulled towards torso, while in late stance, it is in front of the torso and is pulled back towards the torso, so the net effect on the torso is likely to be small but complex. With regard to the ground reaction forces acting though the stance leg, I regard these as potentially a source of significant torque acting on the body. In early stance, vertical GRF produces head backwards rotation and the backward-directed horizontal GRF produces head forwards rotation. The net effect depends on the relative magnitude of these effects. In late stance, vertical GRF produces head-forward rotation and forward-directed horizontal GRF produces head-backwards rotation. I will return to discussion the likely net effect when responding to item 4.

    3. Push off with foot behind with body in alignment (starting from the blocks) – creates force along the body line
    I agree

    4. Push off with foot behind with torso upright (pace running) – creates force along the leg line which pushes slightly below the COM causing some rear torque on the torso
    If the leg was a simple peg with no foot and it was connected to the torso only via the hip joint, I would agree with your estimate of the direction of action of the net force transmitted to the body via the leg in late stance (ie it will push along the length of the femur). In that situation, I would expect that the net torque would produce a head back rotation. However when we allow for the fact that the point of support in late stance is far forward along the foot, and that various muscles act to stabilize ankle, knee and hip, I suspect that the line of action of the force will be more vertical than the femur. Furthermore, if there is lean of torso as indicated in classic Pose pictures (eg the famous photo of Dr R running along the seawall) then the centre of mass will probably be forward of the hip joint. So I think the direction of torque due to GRF in late stance will depend on the precise orientation of the various body parts in each individual. This is what I was trying to convey in my statement about the relative magnitude of the torque due to vertical GRF and horizontal GRF. However, I do believe that a sharp flexion of the toes at lift off will provide a push back against the ground, increasing the forward-directed horizontal component of GRF and thereby tipping the balance towards a head-back rotation. You might remember that I proposed something along these lines in my earliest attempts to account for the balancing of gravitational torque in the discussions on the Efficient Running thread on the Fetch website. When the videos of elite runners, Pose coaches and Pose hopefuls all revealed footfall in front of the COG, I decided that this effect of horizontal GRF was probably negligible in most cases. Our discussion here has made me wonder again whether or not it is worth cultivating a strong backwards flick of the toes with the expectation that this might help balance gravitational torque and thereby reduce the need to land in front of the COG.

    With regard to my statement about the swing being initiated by a push, perhaps I was being loose with my use of language. I meant the forward acceleration of the swing leg. I think there are two main actions that generate the forward acceleration of the leg . One is the action of horizontal GRF, the other is the pull provided mainly by hip flexors pulling the leg forward relative to the torso.

  24. Simbil Says:

    Hi Canute,

    Thanks for the explanations, I’m a lot clearer on where you are coming from now and we are certainly not poles apart.

    1. The legs do act to cancel each other, I agree, that is something I overlooked. We can discount the airborne swings I think in terms of forwards/backwards torque.

    2. Your explanation may well be possible but I think there is another way.
    In early stance, there is not necessarily a pull of the forward leg backwards. Instead at this point I think it is conceivable that the leg simply supports the body and allows momentum to guide the body forwards. At midstance, the swing leg is then accelerated forwards and the rearward torque that is generated is balanced by the increasing gravitational torque that appears just after midstance.
    This theoretical model seems to have the advantage that the footfall does not have to be as far forward because the gravitational torque can be countered mostly by swing.
    The concern I have with your balanced running where weight is supported equally ahead and behind whilst on stance, is that the weight baring ahead will cause mechanical braking and must surely be inefficient. I take your point that this is how running appears when videoed though so I suspect correction by swing may only be a mechanism that is practical in accelerated running or sprinting (where braking forces by wind resistance call for more acceleration).

    4. The kind of calf push you suggest would no doubt be more or less vertical, I was thinking more of a glute push which would be more horizontal.
    Regardless, I think a calf push at terminal stance could correct the torque as you outlined and would serve as a force helping the runner get airborne. But, it would be inefficient if coupled with long times on support (the elastic stored energy depletes quickly as you know) as it would just be muscular action rather than the efficient bounce of a stretch shortening cycle. So, coupled with a landing closer to under the COM it might be a good thing. The biomechanics of a calf push off do concern me a little though – the slight twisting at terminal stance coupled with eccentric loading at the knee could be a recipe for injury especially when the foot is further behind the COM at high paces. That of course needs to be balanced against the landing ahead of the COM which has its many injury risks too – the push could be the lesser evil.

    On balance, I still lean towards swing (2) as the preferred torque correction method for accelerated or fast running. For slow pace running I’m not sure – perhaps the calf-push would be relatively safe if the support time is relatively short so that the foot is not too far behind the COM and stretch shortening is properly utilised.

  25. canute1 Says:

    Simon,
    With regard to mechanism 2; I did not state that there is a pull of the forward leg (ie the stance leg) backwards in early stance, though there might in fact be a small amount of hip flexor action after footfall. However, most of the backwards pull occurs before footfall. There is no doubt that momentum carries the torso forwards both before and after footfall.

    I did state that in early stance that the swing leg is pulled towards the torso. In fact Pose emphasizes the importance of this pull, though whereas orthodox Pose attributes this pull largely to the hamstrings, I think that hip flexors such as psoas make a major contribution. I think we both agree that by mid-stance the swing leg is accelerating forwards.

    However the core of our disagreement is the fact that I do not consider that acceleration of the swing leg in mid-stance can balance gravitational torque. Gravitational torque acting in late stance acts to increase the net head forward angular momentum of the body. If a face down crash is to be avoided, it is necessary to apply a torque that generates a head backward angular momentum. By virtue of the law of conservation of angular momentum, the net angular momentum of a body can only be altered by interaction with a force external to the body. Action of muscles within the body to accelerate the swinging leg cannot alter the net angular momentum of the body.

    There are only three external forces that act on the body when running:

    Wind – a head wind will oppose gravitational torque.

    Gravity – as you know I consider that gravitational torque acting in early stance plays the major role in counteracting the opposite gravitational torque generated in late stance.

    Ground reaction forces (GRF) – as I discussed in my response yesterday, I consider that forward directed GRF acting in late stance might contribute a little to opposing gravitational torque, though on the basis of observational evidence I believe this effect is small. I am perfectly happy to accept your proposal that the gluteals might be capable of a powerful horizontal push to evoke horizontal GRF, but force plate does not reveal a major forward GRF at immediately before lift-off so I do not think that horizontal GRF is the major source of the torque that counteracts gravitational torque .

    So we are left with the core disagreement being about whether or not muscle action that accelerates the swing leg forwards in mid swing can change the body’s angular momentum. I believe this would violate the law of angular momentum, and therefore I reject mechanism 2. .

    On the other hand, the observational evidence of footfall in front of the center of mass seems to support my belief that it is gravitational torque in early stance that neutralizes the gravitational torque exerted in late stance. You object that this will cost energy. This is true but whatever mechanism is employed to counter gravitational torque, it will cost energy. Fortunately, if one spends only a short time on stance, the price of gravitational torque is low (in fact it might be almost be described as red herring), though of course the cost of getting airborne is huge. Running fast is hard work.

  26. canute1 Says:

    Simon,
    You might be interested in the Wikipedia article on angular momentum. http://en.wikipedia.org/wiki/Angular_momentum The key sentence is perhaps: Angular momentum is conserved in a system where there is no net external torque.

    • Peluko Says:

      Hello.

      You say:
      ‘The key sentence is perhaps: Angular momentum is conserved in a system where there is no net external torque.’

      I’ve been reading this discussion (by now not in very deep), and I’ve found that this sentence is correct but you are applying it incorrectly. In general, and of course while running, we are surrounded by gravity, and gravity is an external force to the running body. So gravity provides a net which can be used to generate the ‘net external torque’ need to change angular momentum. While airborne, changes in limb extension and position can change the angular momentum. This is what you use to get alignment when jumping into a swimming pool, for example.

      • Peluko Says:

        Oh s**t!! Delete it!! My fast fingers betrayed me.

        If gravity is equal in every point of the rotating object, it doesn’t affect the angular momentum.

        Changes in limb extension and position can change rotation speed, but can’t influence in angular momentum, even at the gravity presence!!

        I’m sorry…

      • Peluko Says:

        Hello again.

        After my last mistake, I continued thinking about the swimming pool jumping, and I think I’ve found where the ‘net external torque’ comes from. By moving our limps we can affect the angular momentum, and when we move our limps we are putting an external force to the system!! To move our limps we use the energy generated by our metabolism, which translates in forces which didn’t exist when the angular momentum was created. Is like moving us in a wheel chair by creating inertial forces moving our legs. The inertial forces are external to the system in the sense that they weren’t there when the system was created. The forces came from the energy generated in our metabolism.

        Thus this ‘external’ inertial forces can be used to alter angular momentum while we are airborne.

  27. Simbil Says:

    Hi Canute,

    Thanks for the comments and focusing the discussion down to the pertinent area, It seems we do differ mainly on the point of how angular momentum is balanced in running. I’ve had a long day at work but will try and better explain my position.

    I understand your point about conservation, apologies if I am appearing dense! When the leg is swung forward then it must at some point be swung back and overall their would be no net angular momentum change in a full cycle. It is a very compelling argument and I would agree entirely if we were discussing a simple supported pendulum in a vacuum or indeed an astronaut simply swinging one leg back and forth on some airless 1g planet.

    However there are 2 points about running that make it very different from a simple balanced system. The first is as you say the external force of wind resistance acting both against the initial swing (making the swing more forceful than it would need to be in a vacuum) and also in late swing again helping deceleration. Further, the leg tends to extend at the knee as the leg swings forwards and increases the surface area further eroding its momentum.
    You may argue that the wind resistance would be minor – I would need to do some rough calculations to see if it actually makes much difference to give significant asymmetry between the forward and backward leg swing torques.

    The second and crucial factor is that one swing is unsupported (the rearward one) and the other is supported (the forward one). By supported, I mean that the none swing leg is grounded.
    The forward swing whilst on stance is supported so has the needed external force. A forward swing of the leg at any point on stance pushes/pulls the hips backwards. Whilst swinging on stance, the hips cannot move backwards in a linear fashion or develop angular motion around the hip because the support foot is on the ground and friction resists the rearward impulse at the foot. This basically creates a lever so the whole body undergoes rearward angular motion around the foot as if pushed backwards at the hip. The support foot is in effect providing an external force in the shape of GRF that has a component that acts in the forwards direction from the foot. This is also consistent with measured force plate data (Cavanagh and la Fortune) that shows a forwards acting GRF between mid-stance and early terminal stance.
    The later reversal of the forward swing leg produces temporal changes in relative angular momentum of the torso around the hips and no net effect. Any rearward torque in the body caused by the initial swing could not be reversed at this point and so there is no balanced effect of canceling torques by swing alone as there would be if the leg was swung backwards and forwards whilst the other foot was grounded (our astronaut).
    Hence my assertion that you could not swing your leg without gravitational torque. Intuitively this is obvious – if you lean back a little and then swing one leg forwards you will fall over backwards (if you maintain alignment) whereas swinging your leg whilst leaning forwards produces opposing torques and if done properly, balance i.e. no angular momentum acting around the support pivot point.
    I don’t see any violation of conservation laws there: the swing and gravitational torques are balanced between mid and terminal stance, there is no uncorrected angular momentum.
    Ah, what about the angular momentum of the forward swing leg though you may ask? The reversal of the swing leg coincides with the first phase of the forward swing of the rear leg whilst the runner is airborne. In this way the rear leg moves forwards as the forward leg moves rearwards until the forward leg makes ground contact. Once on stance the runner goes into past mid-stance and into the balanced gravitational torque swing.

    A runner with poor postural strength or co-ordination/perception is unable to resist the rearward force at the hips when the leg is swung forwards and instead loses alignment forming the dreaded ‘k-bend’ posture where the hips are back relative to the shoulders and feet..

    Regarding your assertion that any correction of torque is costly, I agree. The obvious benefit of correcting torque by swinging the leg forwards is that the leg has to be swung forward to run anyway, so it is not an additional cost unlike landing ahead which produces unavoidable mechanical braking.

    With regard to your point about the glutes, on refection I think they can only act to stabilise the torque that centres around the hips i.e. trunk stabilisation, in tandem with the illipsoas. That is obviously important but different from the torque that acts around the support foot so I will leave it aside for now as it gravitational torque that is the issue at hand and other considerations may just muddy the water. Correct me if you think it is important.

    We agree on getting airborne as the single biggest cost in running, again that does not seem directly relevant to gravitational torque though.

  28. canute1 Says:

    Simon,
    First let’s deal with the two less crucial issues:

    1) Wind: One basis of direct experience, I believe that a strong headwind can exert a torque of similar magnitude to gravitational torque. There have been times when running into a head wind when I have deliberately increased gravitational torque to help me drive forwards against the wind. When the air is still relative to ground, I suspect the effect of air-resistance is relatively minor, but not completely negligible.

    2) Exerting a backward directed force to evoke forward GRF in late stance: Irrespective of whether my initial suggestion of toe action or your initial suggestion of gluteal action was the better proposal, I think we both agree that in practice the contribution of forward GRF in the final few milliseconds of stance is usually quite small. We shall return later to the issue of the forward GRF in the period shortly after mid-stance

    As we both agree the major issue of contention is whether or not the main mechanism that balances gravitational torque is the swinging leg (during the stance phase) or landing in front of the centre of mass.

    You propose a mechanism by which the swing creates a forward directed GRF after mid-stance. You quite correctly point out that the force plate data published by Cavanagh and Lafortune shows an appreciable forward directed GRF. I believe that the main generator of this GRF is the reaction against the push downwards and backwards due to release of elastic energy stored in the first part of stance. I doubt that muscle action associated with forward acceleration of the swing leg contributes a great deal to this. However, for present purposes, it doesn’t really matter what action generates the forward GRF after mid-stance, since the force plate data show clearly that it occurs. The crucial question for our present discussion is whether or not this forward GRF is likely to account for the balancing of gravitational torque.

    As I have mentioned in my responses in recent days, horizontal GRF after mid-stance will tend to produce head-backwards torque. However, before assuming this balances gravitational torque, we need to take account of the torque due to the vertical GRF. The force plate data of Cavanagh and Lafortune demonstrate that vertical GRF is much larger that the horizontal GRF at virtually all times during stance. After mid-stance, vertical GRF tends to produce a head-forwards torque. As I discussed previously, we would need to have information about the orientation of the leg and foot as well as the magnitudes of vertical and horizontal GRF in order to compute the net torque due to GRF after mid-stance. I suspect it will depend on the precise geometry of each individual runner as to whether or not there is a net torque in one direction or the other attributable to GRF after mid-stance. It might even be that one could learn to adapt the orientation of ones leg and foot to produce an appreciable head-backwards torque, though there might be a danger that this would tend to weaken the force available for getting airborne – which we both agree is of paramount importance. I think that the evidence from observation of videos of elite runners is that they deploy their resources to become airborne, and accept the relatively minor cost of landing a short distance in front of their centre of mass to balance gravitational torque.

    • Peluko Says:

      ‘As we both agree the major issue of contention is whether or not the main mechanism that balances gravitational torque is the swinging leg (during the stance phase) or landing in front of the centre of mass’

      Have you take into account the action-reaction force of the rear foot and leg? During stance phase, foot speed relative to ground is 0, and just after the foot leaves the ground we need to pull to get it forward, accelerating it to reach the next ground contact position. This pull, by the action-reaction principle, generates a deceleration of the full body while it’s airborne. To counteract this pull we need to apply some kind of forward force.

  29. Simbil Says:

    Hi Canute,

    As you say vertical GRF will produce a forwards torque and forward GRF a rearward torque and the magnitudes are key.

    A quick look at the force plate data shows that the maximum forward GRF is around 0.5 x bodyweight and corresponds to a point where vertical GRF is around 1 x bodyweight. I think the maths would show that the deviation from vertical (foot to COM) would need to be 30* or more to make the vertical GRF induced torque greater than the horziontal GRF induced torque, though you may want to check my off-the-cuff intuitive arithmetic there.
    The force plate data was collected in a study of steady pace running if I remember correctly and as such we would not expect to see large deviation from the vertical at terminal stance. I’d expect 15 to 20* at most, that being the case, it would seem the horizontal GRF induced rearward torque would be the stronger.

    If we instead look at the point where the vertical GRF will produce the largest torque, from the GRF graph we see max vertical GRF at midstance but without the grounded foot being behind the COM, no torque is produced and as the foot moves behind the COM, we can see that the vertical GRF drops off steeply. It looks like there would only be something like 5* of deviation whilst vertical GRF is high. Such a small deviation produces very low torque as you will know from your calculations looking at gravitational torque at those kind of angles.
    So I think that the forward torque induced by vertical GRF will struggle to match the torque induced by the horizontal GRF at any point between mid and terminal stance. I’m happy to be proven wrong by some actual calculation here though 🙂

  30. canute1 Says:

    Simon,
    You present evidence indicating that at one particular point in the gait cycle, the net torque due to GRF acts in a head-backward direction. However to demonstrate that the net torque due to GRF acts to balance gravitational torque you need to determine the net torque due to GRF integrated over the entire gait cycle.

  31. Simbil Says:

    Canute,

    OK, lets consider a 3 point plot from 100ms, 125ms and 150ms.

    GRFv 2.5, 2.0, 0.8
    GRFh 0.2, 0.5, 0.4

    I’d estimate that the angle of deviation from vertical at 100ms would be 5*, 125ms 10* and at 150ms 15*.

    If you agree with that we could look at these 3 instants to get an idea for the relative magnitudes of the torques.

    If you have a better method I am open to suggestions.

  32. canute1 Says:

    Simon, I do not have the Cavanagh and Lafortune data to hand any longer. If you could send me the link, that would be very helpful.
    Thanks

  33. Simbil Says:

    I’ll check tomorrow if I have any of the tables to take some of the guesswork out of reading the graphs.

  34. canute1 Says:

    Thanks for posting the data. As I feared from my memory of this data, this looks like a recording from a heel-striker, with a prominent sharp early peak, so a reliable integration will have to be done at closely spaced intervals.
    If we wish to test the hypothesis that net torque due to GRF might account for an appreciable part of gravitational torque we must compute the net value across the gait cycle. It will be important to represent the contribution of the early peak accurately, especially as some of the gravitational potential energy that was consumed in creating this peak will be stored as elastic energy and recovered later during stance, contributing to the forward directed GRF after mid-stance – although whether or not there is efficient recovery of stored energy is not the crucial issue. If the energy was not recovered from stored elastic energy, the runner would have been obliged to exert a backwards and downwards push to compensate for the loss of energy.
    It would clearly be better for the purposes of testing the hypothesis to have data from a Pose runner, but as we have mentioned in our previous discussions, such data is hard to come by. I was disappointed by the lack of enthusiasm for obtaining such data during the Pose weekend at Loughborough.

  35. Simbil Says:

    Hi Canute,

    Regarding Pose research, there was a recent study and you can see it here: http://w4.ub.uni-konstanz.de/cpa/article/view/3291
    Although force plate data was measured, it is not displayed in the document, only maximal GRFs are noted on the graphs. Very interesting nonetheless.

    Regarding the graph I posted, from memory there were heel and mid-foot runners. I will see if I can get the details.

  36. canute1 Says:

    Simon
    The recent study by Fletcher, Dunn and Romanov, to which you refer, is of the accelration phase, which as we have disussed, presents somewhat different issues and is of limted relevance to distance runners.

    If the data from Cavanagh and Lafortune are from a range of quite different runners, we will probaly also need to allow for intra-indivdual variability in estimating the reliability of any calculation. I presume the hatching on the figure you posted provides an indication of intra-individual variability, but it is going to be a tedious job to do a good calculation

  37. Simbil Says:

    Canute,

    Yes, I just posted the Pose one to show that there is research and it is interesting in its own right. It has no direct relevance to the question at hand.

    Regarding the link to the force plate graph, I can confirm that it is for mid-foot runners at a constant 6 min mile pace.
    The complete study does include a heel strike graph and it has a much more pronounced early peek of vGRF than the one in the link above.
    The hashed area covers the range of values for each subject, the line is the average value.

  38. canute1 Says:

    Simon
    It is good news that this force plate data is for mid-foot strikers, as the question of elastic recoil or the need to push down and back to compensate for the initial braking would be greater with heel-strike data. Nonetheless, even for mid-foot there is appreciable backward directed GRF in early stance which will produce a head forward torque and hence evoke a compensatory head-back torque after mid-stance. Hence to demonstrate that the horizontal GRF after mid-stance could be compensating for gravitational torque, it will be necessary to compute the net torque due to GRF by integrating over the entire gait cycle. I think this should be done using 2ms steps to ensure a reasonably accurate coverage of the effects due to GRF in the first 20ms

  39. Simbil Says:

    Canute,
    Maybe we should divide the effort – I will make a 2ms table if you can then process it?

  40. canute1 Says:

    Simon, That seems to be a reasonable division of labour. I will need to know mean velocity, and, if availble mean height and weight, though I could estmate height and weight- these values will not affect the calculation of relative torque, though they will influence absolute value of estimated angular momentum

  41. Simbil Says:

    Hi Canute,
    The velocity of runners in the study was 6 min mile pace (4.12 to 4.87 m/s) but there is no data for height and weight – will have to assume average sizes and weights for runners.
    From the graphs I can give vertical and horizontal GRF in relative to body weight at 2ms intervals.
    The angle of deviation from foot to hip is not available so would need to be estimated.

  42. canute1 Says:

    Peluko
    I do not believe that it is possible to impart angular momentum to a free body from forces acting within the body. When we dive into a swimming pool we usually impart angular momentum to the body by unbalancing at take off. Once airborne, we can change the velocity of angular rotation by internal re-arrangement (eg curling the body into a ball increases angular velocity because the moment of momentum (the angular equivalent of mass) is of a curled up body is less than an opened out body. Conservation of angular momentum required that angular velocity increases as the moment of momentum decreases in the absence of an external torque acting on the body.
    Simbil
    I hope to have time next week end to do the calculations on the force plate data. I have been rather busy this week – at work and also in responding to the many interesting comments on my recent posts and also to some of the postings on Pose Tech

    • Peluko Says:

      Hello again. Maybe my example of diving is not the better example. I’ll try to explain myself.

      You can’t change angular momentum without external forces to a system, that’s ok. But for external you are thinking about external to the body. For external you must consider any force that isn’t there when the angular movement is initiated. This conservation of angular momentum is a consequence from the more generic law of conservation of energy. But when you move your limbs, you are adding energy to the system, and this energy is converted to kinetic energy and then can be converted to inertial forces.

      Lets do some experiments.

      Start with Newton’s first law. A body can’t change its speed in absence of external forces. Sit on a wheel chair. You and the wheel chair are a system in this context. Without touching anything out of the system, push your body forward quickly and stop suddenly. Sure you and the chair moves forward. Where came the external force from? Well, it’s from the inertial force of your body moving forward and stopping suddenly. And to generate this force you introduced energy into the system by burning some fat or some carbohydrates. So the forces are external to the system and produce a work, a change of speed and a displacement.

      For angular momentum it’s the same. Sit on a desktop chair (the one with little wheels and that you can rotate the seat). Keep your feet on the air and start moving them quickly opening and closing your legs. I’m trying it now and I’m surprised about how little leg movement I need to start rotating. And it’s easy to control rotation, accelerate, decelerate it and change its direction. I’m changing my angular momentum using only forces within my body… but they are external forces, introduced to the system by burning carbohydrates.

      Another example is a child’s swing (I’m not sure if ‘swing’ is the word, I’m talking about a rope tied to a tree’s branch forming a U form and a child sitting on the low part). You can introduce the swing movement just by moving your legs and your body, generating inertial forces. You don’t need someone to push you.

      This is the kind of external forces I’m talking about. When someone is running it’s body is constantly introducing energy into the system, and producing inertial forces that can change speed and angular momentum, while airborne or not. While airborne we are swinging our legs and our arms, generating inertial forces, and sure it’s a hard task to calculate which forces compensate mutually and which forces affects angular momentum and which forces brakes or accelerates the forward movement.

  43. Simbil Says:

    I can’t see Peluko’s posts here? Hello Peluko, I agree with Canute on the effects of rearranging limbs when there is no contact with the ground. The only thing I would add is the stuntman effect – continuous accelerated wheeling of the arms will cause the body to rotate in the opposite direction. Net angular momentum stays the same as when the stuntman left the ground though – its just a redistribution.

    Canute, I’ll try and get you the data before the weekend. I’ve been swamped this week at work too.

  44. Peluko Says:

    Hello Simbil. You can’t see my posts?

    Well, now I’m rotating my desktop chair without touching anything external, just by moving my legs. Try it, sure you can also. With a bit of practice you could start rotating, stop, and change direction. Also you can move forward and backwards. Just by the inertial forces introduced in the system by moving your legs. This forces are external to the system because they are generated with the energy from burning carbohydrates, so this doesn’t violate the law of conservation of angular momentum. The angular momentum is changed by introducing external energy into the system (although the energy is ‘internal’ to the body, it’s external in the sense that it wasn’t there before).

  45. Simbil Says:

    Hi Peluko,

    I cannot see your posts on this page, but I can see Canute quoted you and I saw e-mail notifications of your posts on this thread. Very strange.

    If I use my legs to try and spin my chair, I can only make short motions where my legs go one way and I spin the other way and then both legs and chair stop. I cannot make a net torque that makes me spin continuously. If you can, please explain how.
    You are using energy (burning carb) to rearrange the position of your limbs – you are doing work against inertia if you like. I can’t see how you could produce a net torque though without interacting with something else (floor, wall, air resistance etc.).

  46. Peluko Says:

    Simbil, if you move and the end position is not the same that the start position, you are creating a rotational torque and stopping it, all with the same movement. With this kind of inertial forces is tricky to control the end result, but it can be done. For me what works best is to put my legs straight forward and move my feet in a elliptical motion. This generates a continuous rotational force. When it’s enough to break the chair friction, I bend my knees and, for the conservation of angular momentum, I get some more speed (of course, I’m talking about small speeds, maybe a complete revolution in 15 or 20 seconds).

  47. Simbil Says:

    Peluko,

    The good news is, I can see your latest posts 🙂

    I suspect that your office chair spins more easily than mine. If you are managing to impart a net torque then you must be pushing against something. As you are doing circular motions, maybe you are pushing against the air or maybe your body is moving in such a way that it creates more friction on the chairs barings whilst you move your legs one way and less when you move your legs the other way so in effect you push off the chairs own friction. Either way, I think the overriding principle remains the same that you cannot effect your net angular motion without using an external force.

  48. Peluko Says:

    Hello. I’m now trying in my workplace’s chair (nobody is watching 😉 and here I can’t keep the chair rotating after I stop my legs, and is harder to start moving by using only my legs. But if I move my whole body I can rotate in a series of quick pulses. Like when you move the whole chair forward or backward by quickly moving your body mass without touching the ground. I think that the quick pulse movement and the inabilty to produce continous movement is due to some form of force cancelation.

    But I think there is a clear evidence that some kind of work is done, and this work can change angular momentum, at least while the inertial forces are unbalanced. Let me explain.

    When I move this way, my final rotational position is different from my initial rotational position, so in some point of the movement I’ve created a rotational torque, which means an angular momentum, and at other point I’ve created an inverse rotational torque which annihilates the initial angular momentum. So I’m varying the angular momentum over time just by introducing muscular energy in the system.
    The visualization is easier with linear movement. When you use the body movement to push the chair forward, lineally, it’s almost the same. Sure you can move your chair to your desk without touching the ground. You start at a position, then move to another position. Initial and final speeds are 0, but the energy introduced by your muscles produced a force that first accelerates and then decelerates the body-chair system, thus this energy have produced a work (the displacement).

  49. Simbil Says:

    Hi Peluko,

    The linear example is good as it is easier to show what is happening there.
    If you lean forward slowly in your chair it produces a reactive force that pushes back on the chair. Because you are leaning forward slowly, the friction of the chair against the ground is enough to stop the chair moving.
    Now if you lean backwards very quickly, the reactive force at the chair is sharp enough to overcome friction and the chair moves forwards and will continue to roll along forwards a little. So in that way, you can use the external force of friction to impart net momentum into the system.

    It’s the same if you are on a bike or a skateboard – you can lean forwards slowly and then lean backwards quickly to produce asymmetric impulses that result in net propulsion. The key to this mechanism is the external force of friction though. If you are in an environment with no external forces, say floating in deep space, you can not change your net momentum by moving your body. So the basic principle of the necessity of an external force to change a body’s net momentum holds true I think. The effect of that in running is that the movements of your limbs when airborne have little or no effect on your momentum so will not cause you to rotate forwards or backwards in flight.

    The effect of moving the limbs and especially swinging the leg forwards whilst on stance may well have interesting effects on angular movement and that is as far as Canute and I have got in the discussion.The next step is to do some calculations see how likely these effects are.

  50. Peluko Says:

    Hello again, Simbil. Now I see it. It’s only friction forces. I thought about where goes the energy introduced by muscle effort and I thought that it may generate unbalance in the system. Now I see I was wrong.

    Thanks for the physics lesson!!

  51. Simbil Says:

    Peluko, glad we agree.

    Canute, I’ve got some data together from the force plate graph – before I type it up, what format do you want it in?

  52. canute1 Says:

    Simbil
    That is great. I think the most helpful format would be an excel spreadsheet with time in one column and horizontal GRF in the adjacent column. You could send the document, as an attachment to canutewp@gmail.com

  53. Simbil Says:

    Canute,
    Hopefully get something to you tomorrow.

  54. Simbil Says:

    Canute,
    Just sent through the data to your e-mail.

  55. canute1 Says:

    Simbil,
    Thanks for sending the force plate data. I will present the details of the computation in the calculations page (side panel of this blog) as soon as I can find time to lay it out in an adequately annotated form. Meanwhile, here are the results

    The quantities of interest are the angular impulses (product of torque due to the various forces of interest x time, averaged over the time periods of interest.

    Because the weight of the runners is unknown, I express values of angular impulse in the units of body-weight.metre.sec (instead of the conventional newton.metre.sec). We could assume a typical weight of say 65 Kg and convert all units to newton.metre.sec but this would not affect the relative values of the angular impulse due to the various different forces. I have assumed that the distance from centre of mass to ground is 1 metre, and that this remains approximately constant throughout the time on stance (though for most runners, the COM does fall in early stance and rise in late stance. However I think that errors due to mis-estimate of height of the COM are likely to be smaller than errors due to uncertain estimates of the GRF.

    Due to the approximations involved in the calculation,. I would estimate that the computed angular impulses have an uncertainty of 0.01 units.

    The results are:
    Head-forward angular impulse due to gravitational torque after mid-stance: 0.022 units
    Head-back angular impulse due to gravitational torque before mid-stance: 0.016 units.

    Head-forward angular impulse due to braking before mid-stance: 0.018 units
    Head-back angular impulse due to forward GRF after mid-stance: 0.027 units

    Head-back angular impulse due to vertical GRF before mid-stance: 0.026 units
    Head-forward angular impulse due to vertical GRF after mid-stance 0.024 units

    The conclusion from these computations is that the gravitational torque prior to mid-stance provides about 2/3 of the compensation for the head forwards angular impulse due to gravitational torque acting after mid-stance, while the backward push (that evokes the forward GRF) provides about 1/3 of the compensation.

    However, because of the uncertainty due to the approximations in the calculation and the approximations in the estimate of GRF, it is plausible that the backward push might account for anything from zero to just over half of the compensation for the head forwards angular impulse due to gravitational torque. So the computation does not provide an unequivocal answer to our debate but tends to support the hypothesis that the largest part of the compensation is provided by head-back gravitational torque acting before mid-stance, with a minor part possibly accounted for by the backward push.

    There is one additional point to note about these calculations. GRF produces rotation about the centre of mass, while gravity produces rotation about the point of contact between foot and ground. I am not sure that it makes any sense to claim that the rotation about the centre of mass can compensate for rotation about the point of contact between foot and ground. I need to think about this a little more, but I am inclined to think that these two angular rotations have to be compensated separately. If so, the small difference between the computed rotational impulse due to gravity before mid-stance and that after mid-stance is likely to be a measurement error – or maybe due to wind resistance. Where the force plate data collected on a treadmill?

  56. Simbil Says:

    Hi Canute,

    Thanks for running the calculations and sharing the results. I’ not sure if your calculations were for hGRF only or both hGRF and vGRF? It would be nice to have the complete picture.

    From a look at the hGRF graph, I’d say around a 1/3 difference between head back and head forward torque would sound about right. The graph looks almost like a squashed sine wave with but with the noticeable asymmetry in the first half of the gait where the hGRF does not peak but instead drops and then rises again to form to small peaks.

    With regard to your point about head-wind, these trials were carried out outdoors rather than on a treadmill so there will be wind resistance and as the runners were at 6 minute mile pace it will not be negligible. However, I wouldn’t expect it to account for all the difference either between head forwards and head back torque via hGRF.

    With regard to your point about the first half of stance being the most significant in balancing the torques, I’ll wait until it is clear if you considered both vertical and horizontal GRF in your calculation before commenting.

    Regarding your last point about the pivot point of the torques, this is an area that needs careful consideration.
    I think the hGRF that acts in early stance will produce a head forward torque pivoting around the foot. At the same time there will be a vGRF induced head backward torque also around the foot.
    In the second half of stance the vGRF will produce a head forwards torque around the foot. The hGRF is not so clear cut as it depends on how it is created. If its source is gravity, it will act around the foot. If its source is a muscular driver from the hip then it will have a strong component around the hip. However, if it is muscular involving extension it will act at the foot and if it is muscular involving leg swing it will again act around the foot. On balance, the majority pivot point is likely to be the foot I think.

  57. canute1 Says:

    Simbil, Thanks for clarifying the fact that the data were collected out of doors. I think it is quite plausible that air-resistance accounts for the discrepancy. If linear momentum is to be conserved, the backward linear impulse due to air-resistance together with the backward hGRF in early stance must match the forward linear impulse generated by forward hGRF in late stance.
    It is similarly plausible that the head-back angular impulse due to air resistance together with the head-back angular impulse due to GT in early stance will match the head-forward angular impulse due to GT in late stance.
    Without a precise estimate of air-resistance it is not possible to make an absolutely definitive statement, but I see no reason to suggest that air-resistance is inadequate to account for the discrepancy.

  58. Simon (simbil) Says:

    Hi Canute,

    In constant pace running it seems plausible that air resistance plus braking forces at landing will of course balance with propulsive forces.

    The question at hand though is the torques rather than the linear forces.

    Wind resistance is a force that reacts to movement rather than a constant force like gravity. I agree that wind resistance will diminish the effect of forward acting torques and enhance the effects of rearward torques whilst on stance.

    Data from a runner accelerating on a treadmill, or a runner at low speed (low wind resistance) would show whether wind resistance creates a substantial counter torque. I think the data here http://w4.ub.uni-konstanz.de/cpa/article/viewFile/3291/3092 shows that at modest speeds (4m/s or 8mph), there is a very large discrepancy between foot forward of support compared to foot behind support. This discussion is continuing here https://canute1.wordpress.com/2009/12/31/creating-optimum-stride-length-and-cadence/#comments so I will make my comments there.

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