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 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.

2) Lift -off

At lift off from stance, the ankle is lifted towards the hip. This action is initiated by the recoil of Achilles tendon and assisted by an adjustment in the relative tension in hamstrings and quadriceps that allows the knee to flex.  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 it is probably desirable to initial hip flexion as soon 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.

3) Leg swing

The swinging leg is propelled forwards by flexion of the hip, but the pendular action cannot 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, flexors 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.

 This article was edited in April 2012 to make it more consistent with my posts in the months Jan to April 2012

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.

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5 Responses to “The Mechanics of Efficient Running”

  1. nrg-b Says:

    Your second article is about Mechanics of running:
    – When you say “no propulsive force is required to maintain a constant velocity on a horizontal surface in the absence of wind resistance” what about sound energy of your footfall, energy required to raise the GCM, the inefficient return of elasticity in the lower legs? etc etc.
    – “The art of efficient running entails swinging the leg forward in a way that uses minimum energy with minimal risk of injury” – yes I agree but this is only part of what’s going on. What about the landing and how best to break contact with the ground? Like jonp & jeremey, I would caution the emphasis on swinging the leg as it could lead to overstriding and active landing (ie landing with the calves more tense then required).
    – General Principles:
    – (2) Vertical Motion: “Therefore, to minimize free fall under the influence of gravity, the airborne period should be relatively short.” I think rather then to minimize the airborne period, the ground contact time should be minimized. A shorter ground contact time would increase the physical quantity known as “Impulse”.
    – (3) Yes and No. Mainly Yes. What do you mean by “Lean”? The Pose meaning of Lean is from the support point to the COG. When in mid-stance ie Pose Stance we want to see a nice straight line connecting the support BOF, hip (COG/GCM), shoulder and head. This line will naturally be leaning forward. This is only a snap-shot moment in time. The upper torso can remain upright. “This principle must be set against the fact that a small degree of destabilization of the body from the stance will evoke automatic swinging forward of the leg” – Cool!!! So what causes the automatic swing of the landing leg??? (Answer this and you’ve reached Pose Nirvana!).
    – (4) Cadence. Yep!
    – (5) GRF. Yep !
    – The components of the gait cycle: “the foot follows a quadrilateral path” – hmmmm, my foot seems to follow a sort-of flattened tear drop path???
    – (a) Base Position: But what causes the “reflex swing of the leg”?
    – (b) Ankle Lift: Nope. I think by late stance ie foot about to break contact the achilles tendon and quads have done their work. We are changing support. The body is now in preparation to land on the other leg – with or without mental thought. The hamstring contraction is a point of MENTAL FOCUS. Other muscles are (must be) used. Please note that as soon as we land the trailing leg is being yanked forward. It seems to me that a strong core would allow for a stable hip which means that the new landing leg going back will help transfer some force over the hip to bring the trailing leg forward???????
    – (c) Leg Swing – Yep !
    – (d) Foot fall – “Although voluntary muscle action is not required, a strong automatic stabilizing contraction of the quadriceps must occur to prevent the knee collapsing on impact” – YEP! Hence why I do Hindu Squats to strengthen the Quad Vastus Medialis muscle.
    – (e) Torso: Yep !
    – (f) Arm Swing – Yep !

    Thank you for acknowledging me. I am not worthy since I stand on the shoulders of giants like RW forumites such as Chaos, KJ, AlexS, terryh, Pantman and of course my good mate Nicholas Romanov, who all had a hand in teaching me all that I know.

  2. canute1 Says:

    Nrg-b thanks. You modestly state that you stand on the shoulders of others, but the reason I acknowledged you is that you are one of the many people who have kindly (and at times humorously) stimulated my thoughts on the subject, so thanks for your past comments on the Fetcheveryone discussion thread, and thanks once again for these comments.

    With regard to the various energy consuming processes you mention, I see these as energy consuming processes arising from the need to move the legs forward. The point I was trying to make is that it is not the forward propulsion per se that required energy input (in the absence of external resistance such as wind resistance) but the fact that we must move our legs forward to avoid a face down crash. The reason for expressing it in this way, is that it emphasizes that one needs to work out how to move the legs forward relative to the COG efficiently, rather than employ muscle action directly to propel the body forwards – as I see it, moving the legs forward allows momentum to sustain the forward motion of the body.

    I agree that ground contact should be kept short, in accord with general principles 3) and 5) in my article, but it is also desirable to keep airborne time fairly short to minimise the amount of free fall. This is illustrated by the calculation presented on the calculation page in the side bar of this blog site. Also, if airborne time becomes much longer than stance time, the average GRF during stance must rise, increasing the forces transmitted through the foot. Both short stance and fairly short airborne time can only be achieved by high cadence, a feature of most of the recently proposed forms of efficient running, including Pose, and noted in your fourth point.

    I do not know the mechanism by which the central nervous system generates a reflex action to prevent falling when the body is destabilized, but one would certainly expect either evolution (or God) would have equipped us with protective reflexes of this type. Inspired by F. Matthias Alexander and now challenged directly by yourself, I am pondering the mental processes that evoke motor responses, and will probably post my thoughts on this at some time.

  3. Febble Says:

    Some pictures would be useful. Photos or diagams.

  4. canute1 Says:

    I will try to prepare some diagrams, and also to upload (maybe to the Google video site) a video of me attempting to put my proposed running style into practice. However, first of all I need someone prepared to stand in the cold and hold a video camera

  5. Bill McGuire Says:

    Canute, may I suggest that you find a way to be the first person to present a sophisticated animation of how it all works?

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