The Mechanics of Efficient Running

This is a version of my original post on the Mechanics of efficient Running posted on 29th December 2007, updated as I have obtained more information from comments, observations or reading.

This version was updated on 1st January 2008 and again on 13th April 2012; details of the changes are listed at the end of the article.

This page has been substantially extended by a series of articles under the tile ‘Running: a dance with the devil’ posted in March 2008.  That series attempts to cover the main physical, biological and psychological  aspects of running.

The Mechanics of Efficient Running

This article is a speculative account of how to run with minimal consumption of energy and minimum risk of injury per kilometre. We will start by addressing the question of how to run at constant velocity on the flat in the absence of wind resistance, and subsequently consider how to adapt to wind resistance and hills.

The first principle is that according to Newton’s first law of motion, no propulsive force is required to maintain a constant velocity on a horizontal surface in the absence of wind resistance. The practical consequence is that muscular effort to drive the body forwards is likely to waste energy and increase the risk of injury.

However, it would be misleading to imply that no muscular effort is required. If the feet were fixed to the ground, forward momentum and gravity would combine to cause the runner to crash face-down, so it is necessary to move the legs forward alternately in such a way as to arrest the tendency to fall. In contrast to walking, while one leg is swinging forwards (‘the swing phase’), the other leg is on the ground (stance phase’) for only a part of the time. Thus, for a substantial portion of time the runner’s body is airborne. The effort to become airborne and the impact with the ground at foot strike, create risk of injury. The art of efficient running entails swinging the leg forward in a way that uses minimum energy with minimal risk of injury.

To understand how this is done requires an understanding of what muscular actions are required and what muscular actions are to be avoided. Learning how to do it requires acquisition of the correct sequence of movements, which can be facilitated by use of a specific drill (the swing drill, described in a separate article), and subsequent practice of this sequence of movement until it becomes habitual. In my experience, the sequence can be acquired with less than an hour of practice. Warm-up for each running session should begin with the swing drill and a period of relaxed running focussing on technique. Once the sequence of actions is habitual, execution of the procedure does not require conscious planning of each muscle action, but rather, the use of simple imagery to evoke the learned sequence.

General principles

Certain principles of physics and physiology can be invoked to determine the optimum sequence of actions. The guiding principle is that acceleration or deceleration of the body’s centre of gravity (COG) relative to the ground should be kept to a minimum, because acceleration and deceleration require energy and also have potential for injury. Furthermore, acceleration of one body part relative to another should also be used a sparingly. The following specific principles follow:

1)      To minimise braking, the period of time for which the foot is on the ground in front of the Centre of Gravity (COG) should be minimised.  However, any change in the speed of rotations of the body around the pivot point where the foot contact ground, and also any change in horizontal velocity between footfall and mid-stance (when the COG is immediately above the point of support) must balance the oppositely directed changes that occur between mid-stance and lift-off from stance (in order to  satisfy the laws of conservation of angular momentum and conservation of linear momentum). Therefore if the time on stance with the foot in front of the COG is short, the time on stance between mid-stance and lift-off must also be short.  Thus total time on stance will be short.  To achieve this a relatively large push against the ground is required.   A large push against the ground generates a large ground reaction force (according to Newton’s third law of motion.) and some of the implications of this are discussd in point 4 below.

2)      Vertical motion of the COG should be minimized as downwards motion increases force on the ground and upwards motion requires energy. Nonetheless, during the airborne period, the body is unsupported and must fall. However, because acceleration under the influence of gravity causes a steady build up a speed, the body will fall less during a series of several short airborne periods than during a series of fewer longer airborne periods of the same total duration (See the article on calculations for the mathematical demonstration of this). Therefore, to minimize free fall under the influence of gravity, the airborne period should be relatively short.  However there is a limit as to how short it can be.  The leg must swing forward from its downwards and rearward orientation at lift off form stance to a position in front of the COG  at footfall.  The time available for the swing is the sum of one stance period (while the other foot is on the ground)and two airborne periods.  The swing is a forced pendular action.  Although the duration of the swing can be decreased a little my various strategies such as ensuring the knee is flexed in mid-swing so the pendulum arm is short, even very fast runners can achieve only a modest decrease in swing time compared to less talented runners.  As we have seen, it is desirable to minimise time on stance in order to minimise braking, but the need for adequate time to complete the swing sets a lower limit on the sum of  stance  and two airborne periods, so there is a limit as to how much it is possible to reduce airborne time.

3) If both airborne time stance time should be as short as possible within the constraint of allowing adequate time for the swing, then cadence must be high. Observation of elite runners indicates that it should be at least 180 steps per minutes (i.e. 90 full cycles of the gait cycle per minute)

4) According to Newton’s third law (action and reaction are equal and opposite) the vertical component of ground reaction force (GRF) must be equal and opposite to the downwards force exerted by the foot on the ground. The average value of the vertical component of GRF averaged over the full gait cycle must equal the body weight. As GRF is only exerted during stance, the average value during stance is the body weight multiplied by the ratio of total duration of the cycle to the time on stance. Thus if time on stance is half of the total gait cycle, the average GRF during stance will be twice the body weight. Peak GRF during stance might be considerably higher than this, as the load is not distributed as uniformly over the stance period. However it is desirable that the rise and fall of the load during stance should follow a smooth curve that minimise the likelihood of sharp peaks.  This is probably best achieved by landing with the ankle almost neutral (or with a very slight degree of plantar flexion) so that weight is taken on the mid-foot; then rapidly transferred to the first metatarsal where the energy can be temporarily absorbed by some flattening of the longitudinal arch by a slight roll of the foot towards the inside edge (mild pronation). Some of the energy is stored in the stretched Achilles tendon, whose role includes sustaining the arch. This stretch can only be maintained if the calf muscle is contracted. Finally, the joints of the foot are stiffened by a slight roll laterally (supination) to promote recovery of energy by elastic recoil at lift off. The time on stance must be long enough to allow the transfer of energy between the structures of the foot, but in view of the fact that calf muscle contraction is required to maintain the stored energy, too long on stance will lead to exhaustion of the calf. Thus, consideration of foot dynamics also indicates the need for a relatively short time on stance to optimise the capture of elastic energy. (But if airborne time is much greater than time on stance, GRF during stance will necessarily be high to ensure that average GRF over the entire cycle is equal to weight)

The components of the gait cycle

As outlined above, during the full gait cycle, each foot is engaged in a stance phase and a swing phase. During the swing phase, the foot must be lifted, moved forwards and allowed to drop back to the ground, moving backwards relative to the COG at the point of foot fall. Thus, the foot follows a quadrilateral path, rounded at the corners as each stage of the cycle grades in to the next one. The four segments of the path are:

1) Base position

In the base position the foot is on stance: The COG moves forwards over the foot. According to principle 1) time on stance should be short.  Nonetheless some braking is inevitable as the leg is pressed against the ground while angled forward and downwards prior to mid-stance.  Thus some forward momentum is lost.  In early stance, the body continues to descend but at a deceasing rate as the tendons of the large muscles of the hip and thigh absorb the energy of impact (as described in greater detail below in the description of footfall).  In addition the processes of foot pronation and supination absorb, store and redistribute some of the energy of impact. After mid-stance the release of captured elastic energy initiates the forward and upward propulsion of the body, to compensate for the braking in early stance and to recover the height lost during the fall after mid-flight.   Also, in mid and late stance the calf muscles (especially gastrocnemius) contract to assist in the forward and upward propulsion.

Lift -off

At lift off from stance, the hip and knee joint flex.  The hip flexion initiates the forward swing of the leg, while the simultaneous knee flexion lifts the foot towards the hip. This compound action is achieved by contraction of the hip flexors (largely iliopsoas) and moderate contraction of the hamstrings  together with recoil of the Achilles tendon, which flexes the knee.    Because the hamstrings cross both hip and knee joint, unopposed hamstring contraction would also produce undesirable hip extension which would move the leg backwards behind the line from lift-off point to hip. Observation of elite athletes like Haile Gebrselassie suggests that the ankle should in fact curve upwards in a path that arches behind the direct line towards the hip.  However, the main goal of the swing phase is repositioning the foot in front of the COG in time for the next footfall, and so hip flexion should be initiated as the foot lifts from the ground.   The hip flexion is largely automatic, promoted by recoil of the hip flexors that had been subject to stretching as the leg extended backwards in late stance.   It is helpful to envisage a rapid pulling of the foot from the ground, though of course task of propelling the body upwards had been achieved by the push against that ground that had been maximal in mid-stance.   The contraction of the hip flexors should be completed before mid swing to avoid the risk of over-striding.

3) Leg swing

The swinging leg is propelled forwards by flexion of the hip.  As the thigh swings around the hip joint, the lower leg swings around the knee join. The compound pendular action as assisted by gravity and must not be forced.  In late swing, the hip extensors arrest the swing and the knee extensor partially straightening the knee. However, the knee should not extend fully but remain slightly flexed so that it can help absorb impact at foot fall.

 

4) Foot fall

The foot falls to the ground as the hip swings back towards the neutral position largely under the action of gravity, but with assistance from the hip extensors, with the knee remaining slightly flexed.  Except perhaps when sprinting, it is best to avoid consciously pushing the foot to the ground, as this is likely to result in a mistimed push and might actually delay the subsequent lift-off form stance.   Although deliberate muscle action is not required, a strong automatic stabilizing contraction of the quadriceps must occur to prevent the knee collapsing on impact, while contraction of the hip,extesnors occurs to prevent the torso rotating forwards. Because the hip swings back almost to the neutral position during the fall, the point of impact is only slightly in front of the COG, thereby minimizing any braking effect. The quadriceps absorbs a large amount of energy at impact, some of which will be recovered by elastic recoil to assist in raising the body to recover height lost during freefall.  The contraction of the hip extensors in early stance promote the capture of elastic energy in the tendons of the hamstrings and also the iliotibial band (ITB), which is tensioned  by the gluteus maximus and tensor fascia lata muscles.  The subsequent release of elastic energy from the tendons of the quadriceps hamstrings and ITB around mid-stance provides the main propulsive force that will accelerate the body forwards and upwards in late stance.

The ‘swing drill’ (see separate article) entails practice of the three segments of the swing: ankle lift, leg swing and foot fall, while the body is stationary, supported by the opposite leg.

Torso
Upper body orientation and movement should be used to facilitate the leg movements. The torso should be held in an almost upright orientation, with the pelvis held level and not allowed to drop back.  in a manner that would compromose the backward extesnion of the hip in late stance. The shoulders should be drawn slightly back and rest downwards in a relaxed state. This orientation of the body facilitates a relaxed foot fall to the correct position under the COG.

Arm swing
The arms swing in a minimal arc in a reciprocal action to the leg on the same side. As the ankle is lifted towards the hip the arm moves back moderately forcefully, reflecting the sharp, compact movement of the ankle towards the hip. Then the arm swings forward largely under the influence of gravity, but not in a floppy state, while the leg swings forwards and the foot falls to the ground. If a compact arm movement is practiced during the swing drill, the brain will readily associate the compact arm swing with a compact leg action. Because proprioceptive feedback from the upper limb is more strongly represented in the brain than that from the leg, good form can be monitored more easily if arm and leg are coordinated.

All unnecessary muscle action should be avoided. However in addition to the actions described above there are several other important actions. Reflex contraction of the hip abductors minimizes pelvic tilt and dropping of the hip on the unsupported side. Footfall with slightly flexed knee and the impact absorbing foot action described above would be expected to minimise abrupt loading of the hip abductors while also protecting the knee joint and ankle joint and minimising sharp localized forces on the bones of the foot.

It should be emphasized that this description of efficient running is based in observation a few elite athletes and an attempt to apply the principles of physiology, anatomy and physics as described above, but has only been tested by the author himself. It has not been subjected to any form of controlled trial and hence must be regarded as a speculative proposal rather than a proven method of safe, efficient running.

Acknowledgments

Gordon Pirie, gritty and thoughtful elite athlete, former 5000m and 3000m world record holder and source of inspiration, whose thinking about running style has shaped my own;

Dr Nicholas Romanov, developer of the Pose technique of running, who has emphasised that running style can be improved by thoughtful application of principles;

Cable_Tow, sports medicine specialist and generous-spirited guru on the Fetcheveryone website;

nrg-b: Pose coach with a delightful sense of humour;

Jeremy Huffman, elite athlete and Pose coach;

Jack Becker, generous spirited Pose coach;

Jack Cady, developer of Stride Mechanics;

Haile Gebrselassie, elite athlete, marathon world record holder, and model for efficient running;

Fetch, founder of an amazing website for runners and pace-setter in one of the few races that I have ever won;

Danny Dreyer, developer of Chi running;

F. Matthias Alexander (1869-1955) who showed how changing one’s thinking can re-direct posture and movement, and honed the concept of listening to your body.

Changes from the original version posted 29th December 2007:

1 Jan 2008: The description of the path of the ankle following lift-off was modified to describe that curved upwards path exhibited by elite athlete, HaileGebrselassie

13 April 2012: the general principles were reformulated in a way that is more consistent with the conclusions reached in my posts in the period Jan-April 2012.

27 Responses to “The Mechanics of Efficient Running”

  1. cabletow Says:

    I await the book and DVD with interest.

    I thought you did not buy into the principles of Gravity fed running – There is nothing you have said here that is antiPose and shows that you understand the priciples totally. You do understand the theory – now to apply it in practice – you have become a Jedi master my young Padawan. I bow to to your mastery

    A nice peice of work

  2. canute1 Says:

    It is a special pleasure to receive your comment. You have been my most reliable guide as I have tried to interpret the abundant material in this domain.

    I regard gravity as both friend and foe. I will do a post on my understanding of the role of gravity in running in the near future

  3. Bill McGuire Says:

    This is wonderful. I can’t tell you how much it means to have someone offer real explanations that fill in Pose theory. For a lot of us, “Because I say so” just isn’t good enough.
    The notion of gravity as possible foe is especially interesting. I always felt momentum was a better friend than gravity.

  4. Paulnm Says:

    Ditto to Mark and Bill’s comments above.

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  7. gene Says:

    I tried pose for two months and the gravity and pull technique proved to be a problem for me. I’m thankful i found this site because i was pretty sure a needed some kind of push to get airborne. I will still use part of the pose system, but i will definately push and use my quads

    • canute1 Says:

      Gene,
      Thanks for your comment. Yes, after mid-stance the body must be propelled forwards and upwards. The Pose theory that the propulsion comes for a fall forwards after mid-stance is very misleading. However a large fraction of the energy for this push in an upwards and forward direction comes from elastic recoil. It is not possible to consciously control recoil, but it is possible to develop a mental focus that allows the recoil to occur. So rather than focussing on pushing off, I find it better to visualise rapid lift off. In practice Pose drills can facilitate this, so even though Pose theory is wrong, in practice Pose technique can produce a mental focus that facilitates efficient use of elastic recoil.

  8. Matt McGinn Says:

    Hi!

    I am studying biomechanics at a top 10 university in America. I have been doing semi-extensive video analysis of Usain Bolt’s 9.58 100m (among other finalists at the 2009 Worlds in Germany) recently and have noticed his gait pattern to be similar to what you have described here as well (not surprisingly). One thing that I noticed is after he contracts his hamstring his knee drive is straight forward with his hamstring still fully contracted. This definitely decreases the force required to cause the same amount of moment. Also, tracking his foot motion reminds me of the rods attached to the wheel of a locomotive, not really sure why.

  9. canute1 Says:

    Matt, Thanks for your comment. What you say about Usain Bolt is interesting. I have not examined his gait in detail, but like many sprinters he maintains the flexion of his knee as his hip flexes to bring his leg forwards. Since both the hams and the quads cross hip and knee, I presume this requires a subtle adjustment in the various constituent muscles of the hams and the quads to allow the hip to flex. In addition elastic recoil in psoas and iliacus will help to achieve efficient hip flexion.

  10. mainttobe Says:

    An enlightening article – I put into practice what I had learned from your article (after one quick read) I took a minute off my 5Km run. Wow,

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  12. ken Says:

    Interesting
    So you essentially describe pose….
    Makes sense

    • canute1 Says:

      Pose incorporates many features of good running style. However the theory of Pose is simply wrong. The mantra of Pose, Fall, Pull is not what happens. The centre of mass rises after mid-stance. This is predicted by simple physics and confirmed by observation of video recordings.

      • ken Says:

        So have at it with analysis of Romanov or bolt. Love to see. Better yet let’s see you run and put your.technique in motion..thanks

    • canute1 Says:

      Ken, You can start with fig 11.1 of Pose Method of Running. This is actually a quite good illustration of running, and clearly shows the Centre of Mass rising after the pose at mid-stance, contrary to the mantra of Pose, Fall, Pull

      • Ivan Rivera Says:

        Canute, I’m not quite sure that the “fall” in pose implies a net loss of altitude. For example, if I fall forward from a slightly flexed leg, and extend my leg as my falling angle increases, I’ll probably gain some altitude, particularly because of external rotation and extension of the stance/pushoff hip.

        In any case, as i go from dorsiflexion to plantarflexion, that net gain would probably be exacerbated.

        Referring to this as a “fall” isn’t necessarily disingenuous.

    • canute1 Says:

      Ivan,
      Thanks for your comment.

      Interestingly, an analysis of the changes in angular momentum over the gait cycle employing the simplified model using a symmetrical rise and fall of GRF does indicate that rotation in a forward and downwards direction increases after mid-stance, though the COG is rising at this time. I think this is in accord with your description. Nonetheless, it is not actually a fall in the usual sense of the word and I do believe it is disingenuous to describe this movement as a fall to justify Romanov’s misleading (though vaguely stated) claim that gravity provides forward propulsion.

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  14. Maria C Says:

    Hello,

    I am doing a Physics lab on the efficiency of running at different cadences. I have read a lot of your calculations and findings- they are very interesting and helpful. I am testing this out on a treadmill. To calculate the efficiency, I was planning on using the equation of motion s=ut+ 1/2at^2 as you did and then finding the energy and then the effieciency using efficiency = useful energy out / total energy in. Will this work? I could use any advice you have to offer. Thanks!

    Maria

    • canute1 Says:

      Maria, thanks for your comment.

      I think the answer depends on what you mean by efficiency.

      For the distance athlete, the goal is to minimise the total energy cost of running. When running on a level surface, the main costs are :
      1) Work against gravity to get airborne
      2) Work overcoming the braking effect that occurs when the foot in on the ground I front of the centre of mass
      3) Work to move the limbs, of which the largest part is moving the swinging leg from behind the body to a position in front of the body
      4) The internal metabolic costs within muscle due to the fact that only about 25% of the energy generated by combustion of fuel (glucose of fat) is converted into mechanical work. The rest results in heating the body. The metabolic inefficiency is inevitable because energy is consumed in pumping the various metabolites into the required cellular compartments, recycling some metabolites and removing by-products.
      5) Work to overcome air resistance.

      The efficient runner aims minimises the total of all of these. I do not think the efficiency of a runner should be judged in terms of the ratio of useful work to total work because the definition of useful work depends on your point of view.
      The only net work done when moving the body on level surface is the work overcoming air resistance. No work is done overcoming friction provided the foot does not slip on the ground.

      All 5 of these actions are useful insofar as they enable the human body to move itself faster than by any other means of self-propulsion. Furthermore, in general attempts to decrease any one of these costs results in an increase in another rcost. For example if the runner spends less time airborne, the cost of getting airborne is reduced, but the cost of braking is increased. The goal is to achieve the optimum balance between cost in a way that minimises the total

      I hope you enjoy the physcis lab

      Canute

      • Maria Coffin Says:

        Hi Canute,

        Thank you so much for answering. That makes much more sense now. But it seems since all those actions play into effieciency it may be hard to test. I am looking for a way to measure whether high or low cadence would best benefit a runner. Is there any way to do to physically test this?
        Thanks for all your help,

        Maria

    • canute1 Says:

      Maria

      You will see that I have given some approximate estimates of the mechanical costs (getting airborne; overcoming braking and repositioning the swing leg) in my answer to your question on my post ‘The equations of motion of the runner: efficiency increases with increasing cadence’

      However as I state on that page, the results are only approximate because I have not included the cost of conversion of metabolic energy to mechanical energy.

      I think the most useful way of actually measuring the costs, when running on a treadmill, would be to measure rate of uptake of oxygen. When running in the mid- to upper aerobic zone, most of the energy comes for oxidation of glucose, and there is a fixed ratio between oxygen uptake and glucose oxidation so it is possible to estimate the amount of energy consumed from the amount of oxygen used.

      However you need special equipment to measure oxygen uptake. A similar approach is to measure heart rate. Heart rate rises in approximately in proportion to the amount of energy consumed. (Heart rate – Resting Heart rate)/ Max Heart rate is approximately proportional to the amount of energy consumed. You can estimate max heart rate as (220-age) though this gives only an approximate estimate.

      You might also find that when you ask someone to run at a faster cadence than they are used to, at first they do not recruit muscle fibres with optimum efficiency. The metabolic conversion costs will be higher becauise muscle fibres are not working at their optimum speed of contraction. It takes weeks of practice to achieve maximum efficiency.

      So you need to be cautious in drawing conclusions from any study you do. It is very difficulat to do reliable research into running mechanics, but I think it is good to try. Good luck

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